A light diffusing element is widely used in illumination covers, screens for projection televisions, surface-emitting devices (for example, liquid crystal display apparatuses), and the like. In recent years, the light diffusing element has been used for enhancing the display quality of liquid crystal display apparatuses and the like and for improving viewing angle properties, for example. As the light diffusing element, for example, there is proposed a light diffusing element in which fine particles are dispersed in a matrix such as a resin sheet (see, for example, Patent Literature 1). In such light diffusing element, most of incident light scatters forward (output plane side), whereas a part thereof scatters backward (incident plane side). As a refractive index difference between the fine particles and the matrix becomes larger, diffusibility (for example, a haze value) increases. However, if the refractive index difference is large, backscattering increases. More specifically, there is proposed a technology for placing a light diffusing element on the top surface of a liquid crystal display apparatus so as to enhance the display quality of the liquid crystal display apparatus. However, such light diffusing element does not have sufficient light diffusibility (for example, a haze value of less than 90%), and dose not exert any sufficient effect of improving the display quality. On the other hand, in the case where a light diffusing element having large light diffusibility (for example, a haze value of 90% or more) is used in a liquid crystal display apparatus so as to enhance the display quality, when outside light is incident upon the liquid crystal device, a screen becomes whitish, resulting in a problem in that it is difficult to display a video and an image with a high contrast in a light place. This is because the fine particles in the light diffusing element cause the incident light to scatter backward as well as forward. According to the conventional light diffusing element, as a haze value becomes larger, backscattering increases. Therefore, it is very difficult to satisfy both the increase in light diffusibility and the suppression of backscattering. Further, in an illumination application, as a haze value becomes larger, backscattering increases and a total light transmittance decreases, which degrades light use efficiency.
As means for solving the above-mentioned problems, based on the concept of suppressing the reflection at an interface between the fine particles and the matrix, for example, there are proposed: core-shell fine particles, in which the refractive index of a core is different from that of a shell, and fine particles having gradient refractive indices, such as the so-called gradient index (GRIN) fine particles, in which the refractive index changes continuously from the center of the fine particles toward the outer side, are dispersed in a resin (see, for example, Patent Literatures 2 to 4). However, the productivity of these fine particles is insufficient due to the complicated production process thereof compared with that of ordinary fine particles, and thus, it is not practical to use these fine particles.